It has become increasingly apparent that the Lebanon talks hold the key which might open the door to a wider Arab-Israeli peace. President Hosni Mubarak of Egypt told President Reagan last week that it would be difficult for Arab nations to support the Reagan peace plan for the Middle East as long as Israeli forces remain in Lebanon.
King Hussein of Jordan seems to be looking for signs of progress in Lebanon before he makes his long-expected offer to negotiate with Israel.
But one of the authors of the Reagan peace plan, Secretary of State George Shultz, says ''big gaps'' remain between the governments of Israel and Lebanon and that these gaps are preventing a withdrawal of foreign forces from Lebanon.
Aboard his Air Force plane at the start of a 12-day trip to East Asia, Mr. Shultz gave his most sober assessment to date of the prospects for resolving the Lebanon stalemate. Two of the points at issue are an Israeli proposal for an agreement ''normalizing'' relations between Israel and Lebanon and a demand for Israeli-manned surveillance posts in southern Lebanon to prevent the return of guerrillas from the Palestine Liberation Organization (PLO).
The Reagan administration does not agree with the need for Israeli-manned posts or for any kind of formal normalization agreement.
The administration had hoped to keep its plan for negotiations on the Palestinian and West Bank issues moving separately from the Lebanon issue. But it is clear now that the Lebanon stalemate is halting progress on all fronts.
''At this point, there is a pretty wide gap between the conditions which Israel feels she needs in order to withdraw and the conditions which Lebanon feels are consistent with the emergence of a new Lebanon as sovereign and in control of its territory . . . .,'' said Secretary of State Shultz.
Shultz said it ought to be possible to reconcile Israeli and Lebanese views in a way which provides a ''real insurance policy'' guaranteeing that southern Lebanon does not become a base for attacks on Israel.
The Syrians have said they will withdraw when the Israelis do. Shultz said the US had ''good grounds to believe'' the PLO would withdraw once Syria withdraws.